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Extreme errors of numerical integrations in colorimetric calculations

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Abstract

The tristimulus values of object-color stimuli are commonly calculated by means of the weighted-ordinate method at constant wavelength intervals. By assuming that the tristimulus values are calculated accurately when the wavelength interval is Δλ = 5 nm, we have estimated the extreme errors that can occur when Δλ is increased to 10 and 20 nm. We have also estimated the extreme errors that can occur when other approximate numerical integrations are used, such as Simpson’s rule or Durand’s rule of integration. The extreme errors, are always very large and are caused by jagged spectral distributions of the object-color stimuli included in this study.

© 1975 Optical Society of America

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